2.3 The Composition of Functions Find the composition of two functions and the domain of the composition. Decompose a function as a composition of two functions. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Composition of Functions Definition: Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example Given that f(x) = 3x 1 and g(x) = x2 + x 3, find: a) b) a) Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example Given that f(x) = 3x 1 and g(x) = x2 + x 3, find: a) b) a) Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example Given that f(x) = 3x 1 and g(x) = x2 + x 3, find: a) b) b) Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example Given that f(x) = 3x 1 and g(x) = x2 + x 3, find: a) b) b) Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example Given , find the domain of Solution: f (x) is not defined for negative radicands. Since the inputs of are the outputs of g, the domain of consists of all the values in the domain of g for which g(x) is nonnegative. The domain is Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley